The present invention relates generally to vibrating beams, including piezoelectric or silicon beams that may be piezoelectrically, electrostatically, electromagnetically, or thermally driven, and particularly to vibrating beams that are utilized as force sensors, for example, acceleration sensors or accelerometers. In particular, the present invention relates to a method and apparatus for reducing the forces transferred to the beam supporting structure to thereby improve the mechanical resonance amplification factor (Q) of the vibratory system.
A widely used technique for force detection and measurement in various mechanical resonators, including acceleration, and pressure sensors, employs one or more vibrating beams having a frequency of vibration which varies as a function of the force applied. An electrostatic, electromagnetic, piezoelectric or thermal force is applied to the beams to cause them to vibrate transversely or in various other modes at a resonant frequency. The resonant frequency of such a beam is raised when subjected to tension and lowered when subjected to compression. The mechanical resonator is designed so that the physical quantity to be measured results in tension or compression of the vibrating beam or beams, whereby the vibration frequency of the beam or beams is a measure of the amplitude of the quantity being measured. In one such mechanical resonator, one or more elongate vibrating beams are coupled between an instrument frame and a proof mass suspended by a flexure to measure acceleration. Acceleration force applied to the proof mass along a fixed axis causes tension or compression of the beams, which varies the frequency of the vibrating beams. The force applied to the proof mass is quantified by measuring the change in vibration frequency of the beams.
Recently, mechanical resonators have been fabricated from a body of semiconductor material, such as silicon, by micromachining techniques. For example, one micromachining technique involves masking a body of silicon in a desired pattern, and then deep etching the silicon to remove portions thereof. The resulting three-dimensional silicon structure functions as a miniature mechanical resonator device, such as an accelerometer that includes a proof mass suspended by a flexure. Existing techniques for manufacturing these miniature devices are described in U.S. Pat. No. 5,006,487, METHOD OF MAKING AN ELECTROSTATIC SILICON ACCELEROMETER and U.S. Pat. No. 4,945,765, SILICON MICROMACHINED ACCELEROMETER, the complete disclosures of which are incorporated herein by reference.
In electrostatically driven mechanical resonators, the elongate beam(s) are typically vibrated by a drive electrode(s) positioned adjacent to or near each beam. A drive voltage, e.g., alternating current, is applied to the drive electrode(s) in conjunction with a bias voltage to generate an electrostatic force that vibrates the beam(s) at a resonant frequency. Motion of the beam(s), in turn, generates a current between the electrode and the beam(s) to produce an electrical signal representing the vibration frequency of the beam. Typically, high bias voltages are considered desirable because the current signal from the charging capacitance is proportional to the bias voltage. Therefore, increasing the bias voltage increases the signal to noise ratio of the resonator such that less amplifier gain is required for the oscillator circuit.
Another important consideration in the manufacture of miniature vibratory force sensing mechanical resonators is to minimize variations in the frequency signal from the vibrating beams, except for frequency variations responsive to the applied force. To that end, manufacturers of these devices typically strive to maximize the resonance amplification factor (Q) of the vibrating beams, which generally represents the sharpness of the resonances. The resonance amplification factor, or Q, is typically maximized by partially or completely evacuating the chamber surrounding the mechanical resonator to reduce viscous damping of the resonator beams. Thus, mechanical resonators ideally operate in a vacuum to increase the Q and thereby increase the signal-to-noise ratio of the mechanical resonator.
Various transducers, including accelerometers, utilize one or more vibrating beams that vibrate laterally in the plane of the beams or in various other modes. The resonant frequency of such a beam or beams is raised when the beam is subject to tension and lowered when subjected to compression. The transducer is designed so that the physical quality to be measured results in application of tension or compression to the vibrating beam or beams so that the frequency of vibration of the beam or beams is a measure of the amplitude of the quantity being measured. The performance of a vibrating beam is also degraded if energy is transferred from the beam to other structures, for example, the beam supporting structure, through rotational and transverse forces at the ends of the beam. Such mechanical coupling between the beam and the supporting structure can lower the Q of the beam and cause undesirable frequency shifts. One prior art method used a double-ended tuning fork having multiple beams vibrating out of phase to cancel rotational and transverse forces to reduce the energy transfer from the beam. The double-ended tuning fork utilizes two or more beams located side-by-side vibrating in opposite directions to cancel the forces appearing at the ends of the beams. The out of phase vibrations of the double-ended tuning fork set up equal and opposite reaction forces in the supporting structure at the ends of the beams which cancel. Examples of multiple beam resonators used to reduce energy transfer to the supporting structure are disclosed in U.S. Pat. No. 4,215,570; U.S. Pat. No. 4,372,173; U.S. Pat. No. 4,415,827 and U.S. Pat. No. 4,901,586, the complete disclosures of which are incorporated herein by reference.
Another prior art approach used vibration isolators between the ends of the beams and the supporting structure to reduce the transfer of energy from the beam to the mounting structure. Such isolators usually have an isolation mass at each end of the vibrating beam and a resilient member between each isolation mass and the supporting structure. The resilient members permit the beam and the isolator masses to move relative to the supporting structure, whereby the amount of energy transferred from the vibrating beam to the supporting structure is reduced. The isolation systems are most effective when the isolator masses are large and the isolation springs are compliant. Such large isolator masses and compliance springs result in a low resonant frequency for the isolation system which is undesirable, particularly in accelerometer applications. In addition, isolation systems attenuate the reaction forces generated in the supporting structure, but cannot completely eliminate them.
U.S. Pat. No. 5,450,762, REACTIONLESS SINGLE BEAM VIBRATING FORCE SENSOR, the complete disclosure of which is incorporated herein by reference, provides yet another approach using a counter balance structure at the each end of the vibrating beam to cancel rotational and transverse forces appearing at the ends of the beam, whereby the transfer of energy from the beam to the mounting structure is reduced. The counter balances move in directions opposite to the ends of the beam in order to cancel both rotational moments and transverse forces normal to the longitudinal axis of the beam, i.e. moment and shear forces at the ends of the beam. The action of the counter balance generates equal and opposite reaction forces within the beam that cancel the moment and shear forces internally. Therefore, in contrast to the double-ended tuning fork, the counter-balanced beam transmits no energy into the supporting structure and no reaction force is developed within the supporting structure which must be cancelled by an equal and opposite force. The counter balances are configured relative to the beam to completely cancel only one of either the rotational moments or the transverse forces at the ends of the beam. When one of these forces is cancelled, there remains a residual amount of the other. The counter balance is intended to provide an optimal balance between the amounts of residual transverse force and rotational moment for a particular application. U.S. Pat. No. 5,450,762 also discloses a flexure interposed between the ends of the vibrating beam and the support structure which is intended to reduce the amount of residual torque applied to the mounting structure.
The vibrating beam in the counter-balanced vibrating beam force sensors preferably or necessarily has particular values of four characteristics: (1) beam resonant frequency, (2) longitudinal stiffness, (3) sensitivity to force, and (4) strength. Beam design controls the values of these four characteristics. Often, the manufacturing process makes thickness variation of the beam impractical. Therefore, two dimensions, length and width, are typically chosen to control these four characteristics. While the single counter balanced vibrating beam force sensor of the prior art, shown and described below in FIG. 2, was configurable such that values of the four characteristics of beam frequency, longitudinal stiffness, force sensitivity, and strength, were satisfactory for prior art sized proof masses, shown and described in FIG. 1, some system designs have requirements demanding a larger proof mass. Experience has shown that a larger mechanism with a larger proof mass is less susceptible to interference from various sources and is therefore more stable.
The moment of inertia of the pendulous proof mass and the force from acceleration both increase linearly with the width of the proof mass, while the force from acceleration increases with the square of the length and the moment of inertia increases with the cube of the length. Increasing the moment of inertia causes an undesirable increase in the pendulous proof mass/flexure system resonant frequency. Therefore, the preferred method of increasing the proof mass is to increase its width without changing its length. Such increases in the dimensions of the pendulous proof mass require dimensional changes in the vibrating beams to achieve satisfactory performance. Again, processing constraints do not generally permit changing the thickness of the beams and the four characteristics of resonant frequency, sensitivity to force, strength, and longitudinal stiffness vary differently and independently with variation of the beam dimensions such that control of the four characteristics is often unsatisfactory by mere manipulation of the length and width dimensions.
Generally, satisfactory performance of a mechanism having a proof mass of increased dimensions requires vibrating beams having a force sensitivity reduced in proportion to an increase in the moment of inertia of the proof mass about the bending or hinge axis of the flexure, a strength and longitudinal stiffness increased in proportion to an increase in the moment of inertia, and an unchanged resonant frequency. The resonant frequency of a vibrating beam is proportional to its width and inversely to the square of its length; force sensitivity is inversely proportional to the cube of its width and directly proportional to the square of its length; strength is proportional to its width; and longitudinal stiffness is proportional to its width and inversely proportional to its length. Due to the differently and independently varying nature of the four characteristics with variation of the chosen dimensions of the vibrating beams, no combination of the width and length dimensions result in satisfactory values of the four characteristics for a proof mass of size increased over that of the prior art.
U.S. Pat. No. 5,367,217, the complete disclosure of which is incorporated herein by reference, provides a four bar double-ended tuning fork device wherein two outer beams vibrate out of plane with two inner beams. According to one embodiment, the two inner beams are joined by one or more bridge members extending between the two beams in order to synchronize their motion and eliminate undesirable modes of operation. The four bar resonator operates similarly to the standard double-ended tuning fork described above, except that the beams vibrate out-of-plane rather than in-plane or laterally. The structure taught cannot be adapted to an in-plane resonator and is therefore not applicable to the problems of in-plane. Nor can the four bar out-of-plane resonator be combined with other structures taught in the prior art to solve the problems posed by an instrument having an in-plane resonator coupled to a proof mass of size increased over that of the prior art.